Well, yes and no. You cannot just rename it. The app is encapsulated in the APK, so changing the APK name will do nothing to change the app name you see. You have to go into the APK and change the app name. I have seen a couple of apps on XDA hat say they will do this for you. The app would extract the APK, change the name and recompress the APK file.

You can install Any Cut from the Market. It is free. It allows you to create any shortcut to apps,contacts,etc. on the stock launcher. You can also rename them the shortcut. The icon will be the same as original app.

Thanks for all of the help and suggestions!
I will give a few of these a try (maybe even a launcher). I am another Woot customer... I've had my 16GB Thrive for almost two weeks now. Using "DaleNet-Thrive-HTK55D.31.5.0002-OOM_Rooted_ROM-v1.1"
GREAT forum!!!

Go Launcher EX will allow you to rename your shortcuts- on the "desktop" or otherwise. All you have to do is longpress on the icon and choose "rename". It also lets you resize icons/widgets, etc. I have the paid version though,n I don't know if the free version has this functionality or not.